How to put an Armature in a Book
For this kind of non-organic object, don't parent With Automatic Weight, parent With Empty Groups, it will avoid some bones to influence some vertices they are not supposed to influence. With Empty Groups creates as many vertex groups as bones you have, with the same names, but there are no vertices affected to these groups for the moment.

Once parented, select the vertices you want to assign to a bone, go in the Properties panel > Object Data > Vertex Groups, choose the group the vertices are supposed to be part of (the group that has the name of the bone that is supposed to control that group), and click the Assign button.

You can affect vertices to different bones, and decrease the influence of the group on some vertices with the Weight value under the Assign button. It may be necessary to make the object more flexible.